How to render only a section of the screen?
The VSE Video Sequence Editor and Compositor can offset and clip images already created. These techniques can be animated.      
They can clip one image sequence and write those out to another set of files, another image sequence .  
Of course you can change the camera location to create a whole new set of images.




In case you want to see part of a render without changing the camera the User can use this technique. This seems likely for testing purposes only, yet that is your choice.  This technique saves time because part of the image will be solid or transparent and no further calculation. Above has mentioned that image sequences can be offset and clipped.

The image resolution is &lt;&lt; not changed >>.


View Menu

Render Border

Control-B

Choose the Camera View first. Then keystroke and draw rectangle like box select. Test Render.

I will leave you to explore and search more.
You may be able to do that faster than my time allows me to write a lot of words